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a(n) = number of distinct solutions to the set of equations 1 +- x +- x^2 +- ... +- x^n = 0 over the complex numbers.
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%I #21 Mar 15 2015 20:11:49

%S 2,8,16,64,106,324,696,1856,4046,10240,19084,49152,98110,218140,

%T 464084,1047744,2123446,4718592,9632740,20666444

%N a(n) = number of distinct solutions to the set of equations 1 +- x +- x^2 +- ... +- x^n = 0 over the complex numbers.

%e a(2) = 8 because the set of equations 1 +- x +- x^2 = 0 generates 8 distinct solutions.

%t a[n_] := a[n] = Length[Union[ Flatten[x /. Table[Solve[1 + Sum[(-1)^IntegerDigits[k, 2, n + 1][[p + 1]]x^p, {p, n}] == 0], {k, 0, 2^n - 1}]]]]; Table[a[n], {n, 10}]

%Y Cf. A036289 (total number of solutions to the equations).

%K more,nonn

%O 1,1

%A Josh Locker (jlocker(AT)mail.rochester.edu), Jul 26 2004

%E More terms from _Robert G. Wilson v_ and _Labos Elemer_, Jul 27 2004

%E a(17)-a(19) from _Robert G. Wilson v_, May 05 2013

%E a(20) from _Robert G. Wilson v_, May 05 2013